On Characters and Dimension Formulas for Representations of the Lie Superalgebra
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چکیده
We derive a new expression for the supersymmetric Schur polynomials sλ(x/y). The origin of this formula goes back to representation theory of the Lie superalgebra gl(m|n) and gives rise to a determinantal formula for sλ(x/y). In the second part, we use this determinantal formula to derive new expressions for the dimension and superdimension of covariant representations Vλ of the Lie superalgebra gl(m|n). In particular, we derive the t-dimension formula, giving a specialization of the character corresponding to the Z-grading of Vλ. For a special choice of λ, the new t-dimension formula gives rise to a Hankel determinant identity.
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تاریخ انتشار 2003